[1]} considered extensions of lasso type methods by involving general convex and non-convex penalties. In particular, composite likelihoods penalized by SCAD or MC+ penalty showed interesting properties. To integrate such an idea for the Dantzig selector, we could consider the optimization problem
\(\min \sum _{i=1}^{p}{p_{\lambda _j}(\beta _j)} \mbox{ subject to } {\mu }^{-1}\; \Big |\mathbf {U}_j( \tilde{\beta }) + [\mathbf {A}( \tilde{\beta }) (\tilde{\beta } - {\beta })]_j \Big | \le p_{\lambda _j}^{^{\prime }}(\beta _j), && j=1,\ldots ,p\) 
